Solve 2T=T^2

$$2 T = T ^ { 2 }$$

Solve for T

$$T=2$$

$$T=0$$

Steps Using Factoring

Subtract T^{2} from both sides.

$$2T-T^{2}=0$$

Factor out T.

$$T\left(2-T\right)=0$$

To find equation solutions, solve T=0 and 2-T=0.

$$T=0 T=2$$

Steps Using the Quadratic Formula

Subtract T^{2} from both sides.

$$2T-T^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-T^{2}+2T=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 2 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$T=\frac{-2±\sqrt{2^{2}}}{2\left(-1\right)}$$

Take the square root of 2^{2}.

$$T=\frac{-2±2}{2\left(-1\right)}$$

Multiply 2 times -1.

$$T=\frac{-2±2}{-2}$$

Now solve the equation T=\frac{-2±2}{-2} when ± is plus. Add -2 to 2.

$$T=\frac{0}{-2}$$

Divide 0 by -2.

$$T=0$$

Now solve the equation T=\frac{-2±2}{-2} when ± is minus. Subtract 2 from -2.

$$T=-\frac{4}{-2}$$

Divide -4 by -2.

$$T=2$$

The equation is now solved.

$$T=0 T=2$$

Steps for Completing the Square

Subtract T^{2} from both sides.

$$2T-T^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-T^{2}+2T=0$$

Divide both sides by -1.

$$\frac{-T^{2}+2T}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$T^{2}+\frac{2}{-1}T=\frac{0}{-1}$$

Divide 2 by -1.

$$T^{2}-2T=\frac{0}{-1}$$

Divide 0 by -1.

$$T^{2}-2T=0$$

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$T^{2}-2T+1=1$$

Factor T^{2}-2T+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(T-1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(T-1\right)^{2}}=\sqrt{1}$$

Simplify.

$$T-1=1 T-1=-1$$

Add 1 to both sides of the equation.

$$T=2 T=0$$